Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire

International audienceWe extend to compact Kähler manifolds some classical re-sults on linear representation of fundamental groups of complex projective manifolds. Our approach based on an interversion lemma for fibrations with tori versus general type manifolds as fibers gives a refinement of the classical work of Zuo. We extend to the Kähler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture